Airborne contaminants dispersed in cities, released from industrial accidents, spills, and fires or from the deliberate use of Chemical, Biological, or Radiological (CBR) agents, motivate this work. If there is a significant release of a hazardous contaminant in a heavily populated area, the ability to efficiently provide situational awareness of an incident allows the emergency responder more time to be spent mitigating the problem then trying to understand the output of a less efficient display. The Plume Arrival Time Display that has been developed for CT-ANALYST allows a user to not only efficiently view the incident, but to calculate a faster, more accurate answer than competing solutions. This translates into a faster time to react to a situation, less casualties and the efficient deployment of limited resources. A crisis manager or first responder will usually need to make immediate life and death decisions about how to respond to the airborne threat based on incomplete knowledge of the contaminant source. Even without their dire time constraints, determining wind-driven airflow over a city, accompanied by contaminant transport and dispersion, presents challenging modeling requirements (Boris, J., 2002. The Threat of Chemical and Biological Terrorism: Preparing a Response. Comp. Science and Engineering Vol. 4, 2002, pp. 22-32; Britter, R. E. and S. R. Hanna, 2003. Flow and Dispersion in Urban Areas. Ann. Rev. Fluid Mech. Vol. 35, 2003, pp. 469-496; Patnaik, G. and J. Boris, 2010. FAST3D-CT: an LES model for urban Aerodynamics Model, Proceedings: International Symposium on Computational Wind Engineering 2010, Durham N.C., May 2010). Large, complex-geometry areas and unsteady buoyant flow physics drive computing needs to saturate current modeling capabilities so reasonably accurate runs take from hours to days. Crucial technical issues to be addressed include time-dependent turbulent fluid transport (urban aerodynamics), environmental boundary condition modeling (meteorology), and interaction of the winds with buildings (wind engineering). The advantages of Computational Fluid Dynamics (CFD) using the Large Eddy Simulation (LES) representation include quantifying complex geometry effects, faithfully predicting dynamic nonlinear processes, and reliably treating turbulent dispersion in regimes where experimental model validations are impossible or impractical. The paper, “FAST3D-CT: an LES (Large Eddy Simulation) model for urban aerodynamics” by Patnaik and Boris (2010), considers the performance and validation of such detailed, high-resolution computations and also explains how to make such high quality answers available to crisis managers nearly instantly.
Computational Fluid Dynamics solutions to contaminant transport (CT) can be highly accurate, but are too slow for emergency response and suffer other drawbacks including the need to specify a meaningfully complete initial condition. Therefore, the crisis manager's central dilemma of “fast or accurate” is usually framed by the negative questions: “How slow a run is too slow to be helpful in an emergency?” Or “How inaccurate a prediction might still be acceptable?”However, you can actually have both—speed and the accuracy of a CFD solution. There are applications where computation times of a few minutes or even a few hours might be acceptable but, in a crisis, plume predictions must occur in a few seconds, at most. That is all the crisis managers are really willing to wait. Further, there are also important applications to multi-sensor interpretation and sensor placement optimization that require even shorter computation times.
The U. S. Navy's Naval Research Laboratory in Washington, D.C. has developed Chemical-Biological-Radiological (CBR) crisis management software called CT-ANALYST to solve the critical speed-versus-accuracy dilemma for time-constrained, information-limited users with real operational requirements. CT-ANALYST is both instantaneous (meaning nearly zero computing delay) and accurate. CT-ANALYST is a visual “point-and-click” application and deployable versions of CT-ANALYST are implemented on laptops, workstations and hand-held devices.
Effective defenses of cities, large bases, and military forces against chemical, biological, or radiological (CBR) incidents or attack require new prediction and assessment technology to be successful. The existing plume prediction technology in use throughout the nation is based on Gaussian similarity solutions (“puffs” or “plumes”), including an extended Lagrangian approximation applicable only for large regions and flat terrain where large-scale vortex shedding from buildings, cliffs, or mountains is absent. These current plume methods are also not designed for terrorist situations, where the input data about the source (or sources) is very scant and the spatial scales are so small that problem set-up, analysis and situation assessment must take place in seconds to be maximally effective. Both greater speed and greater accuracy are required.
The CBR defense of a fixed site or region has a number of important features that make it different from the predictive simulation of a contaminant plume from a known set of initial conditions. The biggest difference is that very little may be known about the source, perhaps not even its location. Therefore any analysis methods for real-time response cannot require this information. It is a crucial requirement to be able to use anecdotal information, qualitative data, and any quantitative sensor data available, in order to instantly build a situation assessment suitable for immediate action.
A Discussion of CT-ANALYST: The how and why of Nomografs™ for CTANALYST:
An urban-oriented emergency assessment system, called CT-ANALYST was developed to evaluate airborne Contaminant Transport (CT) threats and aid rapid decisions for regions such as cities where other methods are slow and inaccurate. (Jay Boris, Gopal Patnaik, Keith Obenschein, Laboratory for Computational Physics & Fluid Dynamics, (May 3, 2011) Naval Research Laboratory, Washington D.C. 20375 (2012)).
CT-ANALYST gives both greater accuracy and much greater speed than alternate prediction tools because it embodies entirely new principles to function in the information-starved situations that characterize the first few minutes of a terrorist or accident scenario. CT-ANALYST was designed for the military prior to 9/11 to use verbal and sensor reports, to use mobile sensors, and to function in realistic situations, such as the first few minutes of a harbor spill, where information about the airborne contaminant or Chemical, Biological, Radiological (CBR) agent is highly uncertain. These improvements are made possible by pre-computing very accurate three-dimensional flow solutions that include solar heating, buoyancy, complete building geometry, trees, and impressed wind fluctuations. Detailed 3D simulations for 18 wind directions are pre-computed for coverage regions where CT-ANALYST is to be installed. CT-ANALYST extends these results to all wind directions, speeds, sources, and source locations through a new data structure called Dispersion Nomografs™ (hereinafter “DISPERSION NOMOGRAFS”). We generate these “nomografs” for cities, ports, and industrial complexes well in advance so manager in an emergency need not wait for supporting analyses. CT-ANALYST also provides new real-time functions such as sensor data fusion, “backtracking” reports and observations to an unknown source location, and even evacuation route planning. The resulting capability is faster, more accurate, more flexible, and easier to use than Gaussian and particle-based dispersion models.
I. Introduction
DISPERSION NOMOGRAFS (or just nomografs) are two compact, pre-computed contour maps (data bases) that capture the aerodynamic and turbulent effects of terrain, buildings, vegetation and surface types on the transport and dispersion of contaminant plumes in cities. Standard, well-validated fluid dynamic principles are being used to solve the plume prediction problem in an entirely new way that directly yields the entire “hazard area” at risk of contamination. Most other methods require costly, repetitive computing of many separate contaminant parcels to build up a predicted hazard area. Further, these older methods are only as good as the accuracy of the urban airflow models that they use. With nomografs, improved accuracy and much greater speed are achieved for urban-oriented emergency assessment. By interpolating into these patented nomograf contour maps, we can perform plume predictions and related assessments in milliseconds for wide areas with complex terrain such as cities, ports, and important facilities.
The Naval Research Laboratory (“NRL”) high-fidelity 3D, Computational Fluid Dynamics (CFD) model called FAST3D-CT underpins our current implementation of DISPERSION NOMOGRAFS within the CT-ANALYST software system. FAST3D-CT computes multi-gigabyte 3D, contaminant flow-path databases from which the high-resolution DISPERSION NOMOGRAFS are extracted for a city well before CT-ANALYST is ever deployed. Other models that can provide the same fluid dynamic information could, in principle, also be the source of data to build nomografs. For that matter, if enough data could be taken in field trials or experiments, equivalent to three-dimensional fields of the important flow variables over the region, nomografs could then be made from field data.
This short paper describes the principles behind the use and computation of nomografs for predicting the transport and dispersion of airborne contaminants in cities such as Hamburg. It also compares this new approach to older approximate approaches that use Gaussian puffs, Gaussian plumes, or moving particles to predict the plumes associated with contaminant releases. This comparison is offered to show that the same fundamental airflow information is absolutely necessary in all cases, but that this information can be used much more efficiently and accurately in the nomograf representation under the conditions that apply in the first hour or so of a contaminant release within a city.
II. Common Aspects of Using Transport and Dispersion Models
In an accident or other emergency, the starting conditions for most airborne Contaminant Transport (CT) scenario are very poorly defined. The agent, its amount, the source location, the method of release and the release time may not be known. Nevertheless, a rapid, informed response can be crucial because roughly three-fourths of the casualties will be caused in the first 15 minutes in case of a major rupture or other rapid release. Current CT models take a few minutes to set up and run and thus are too slow to support most crises directly. They are also unnecessarily inaccurate because the building geometry and other local details are largely ignored to reduce the necessary computation. Even if one accurate plume can be computed in 5 minutes, we will need 30 minutes to process reports and sensor readings to find (“backtrack” to) an unknown source location and then to predict the plume's path and consequences. In this time most casualties will have occurred. Furthermore, other, better data will have come in that we can't use without starting over.
In some applications, finding the unknown location of a source from sensor readings and reports may be a crucial issue. In others, such as with ships or rail cars, moving and even multiple sources may be involved. When a source location and release time are uncertain and the winds are shifting, such as with expected biological sources, or when a number of sensors have to be placed optimally, many thousands of plume evaluations are needed. These considerations all suggest strongly that faster methods than Gaussian puff, Gaussian plume, or Lagrangian particle models are needed.
Model accuracy is just as important as speed. All methods for computing contaminant transport must know the average air (wind) velocity at each place where the contaminant goes and must have a useable model of the wind fluctuations (i.e. the turbulence and local gusts) in that region. The building geometry determines the velocities and fluctuations in cities and the detailed terrain geometry, including trees will be just as crucial away from cities. Accurate plume predictions can come only from accurate winds, which require accurate geometry. In the interests of speed, other plume prediction schemes generally use large area winds from external sources, such as weather predictions, or else simple formulae to approximate the airflow with random-walk approximations to mock-up the dispersion. Computing the detailed urban Computational Fluid Dynamics (CFD) while you wait is simply far too slow—even when you do know the source and wind initial conditions.
CT-ANALYST distinguishes itself from other models by using accurate pre-computed wind fields to completely circumvent this speed-vs-accuracy dilemma. In principle, this advantage could also give more accurate predictions cheaply in other plume prediction methods but the accuracy of the wind fields they use is not their only performance drawback. The way they use the wind and turbulence fields is also very inefficient. FIG. 7A and FIG. 7B show two diagrams contrasting how the velocity and fluctuation information is used in Gaussian and particle models (left) and how the same information is used for DISPERSION NOMOGRAFS (CT-ANALYST-right). The small rectangle represents a building interacting with the flow and increasing dispersion.
III. Using Wind Velocities for Gaussian Puff and Nomograf Models
In Gaussian puff models, each puff moves with the wind and has a finite size that grows from the local turbulence. Each puff center is moved during a time step using an average wind velocity at the puff center. In the vertical this average wind velocity is usually computed using knowledge of the atmospheric velocity profile near the ground but the typical horizontal resolution of these winds is one or two kilometers. This is at best a number of city blocks, making accurate treatment of the dispersion caused by urban geometry impossible.
Gaussian puff methods on the left in FIG. 7A use the wind velocity at the puff center to determine where the center moves and use the fluctuations, represented by the arc(s), to determine how much the puff spreads during a timestep. Using nomografs, the left edge of a contaminant plume moves in the direction of the leftward turbulent deflections of the average velocity and the right edge moves in the direction of the rightward deflections. In FIG. 7B, the zig-zag line shows how the left plume edge is deflected around a building.
The Gaussian puffs each have a different, constantly changing, exponentially decreasing “Gaussian” density profile that they carry around with them. Each profile approaches zero in the outer regions of the puff, as indicated by the shading of the orange ellipse in the figure above. This puff profile is the exact solution of a diffusion equation for the puff material (gas or particles) when the wind velocity and turbulence are constant everywhere, but this is only a crude approximation at best. When the puff is small, its motion and spreading results from distortions, vortices, and local shear flows and these are not well represented as diffusion. When the puff is large, diffusion becomes a more correct physical model but the turbulence and velocity are quite variable across the puff. The overall contaminant density at any time is computed as the sum of all these individual density profiles at each point.
By way of contrast, the panel on the right in FIG. 7B shows how the local average velocity and turbulent fluctuations (arc) are used in CT-ANALYST via nomografs. Two composite directions are computed for the contaminant plume, the limiting direction that the right edge would take, and the limiting direction that the left will take. These directions will be the same when the velocity is completely steady; the contaminant then moves with the wind but does not spread. However, when the actual velocity at each point is fluctuating due to turbulence, there is a maximum displacement of the contaminant to the right of the average velocity and there is a maximum displacement to the left. In this approach, the entire plume is defined between the limiting right and left edges, and these edges can be computed as simple one-dimensional integrals. Since the velocity fields, pre-computed using the FAST3D-CT code, are typically resolved to 5 or 6 meters, the geometric accuracy of these edge calculations is far higher than can be approximated by Gaussian puff, particle, or plume approximations.
FIG. 8 schematically indicates the beginning of the detailed solution procedure for Gaussian puff models. Many puffs, a few each time step, are generated in the source region and are moved away downwind. A number of time steps are used to track each puff as it moves and expands. These timesteps are extrapolations mathematically and so become less accurate the longer the steps are. To improve accuracy, puffs are split up when they become too large, a process that slows computation. To save unnecessary computer cycles, puffs are also merged when there are a number of them overlapping. This necessarily reduces accuracy and increases program complexity.
As illustrated in FIG. 8, a sequence of Gaussian puffs original at the source circle on the left and move along the average wind direction indicated by the curved black line. These puffs spread according to the strength of the velocity fluctuations along the puff centerline. This spreading is indicated by the change in size, as each succeeding puff gets larger.
The important prediction in most crises is the expected hazard area to avoid. FIG. 9 shows schematically how this Gaussian puff information is used to compute a hazard area, indicated by the red line, for the overall plume. This line is generally defined where the summed density of the outermost puffs drops away below some predetermined threshold or where some health consequence is minimal. Each puff has its own density profile that can be expensive to compute; each of these profiles is fuzzy; and these profiles all overlap everywhere. Therefore, to find the hazard area for the plume, conventional models must add the profiles together at each point to get the composite density before identifying, within the fuzzy plume boundary, what defines a particular hazard area.
Referring to FIG. 9, the hazard area for the plume is shown as the circumferential line drawn around the summed density profile of all the puffs at a specified threshold value. This value depends on a definition of the hazard or health consequences that may require appreciable extra computation.
When different sources of contaminants interact, it is necessary to repeat the above procedure for each source and the overall procedure is very slow, generally taking minutes to compute even on today's computers. The procedure is also relatively inaccurate because the underlying mathematical assumptions are questionable in the urban context and because the wind fields are neither accurate nor well resolved.
IV. Fluid Dynamic Principles Used in DISPERSION NOMOGRAFS
FIG. 7A and FIG. 7B above showed schematically how the local average velocity and turbulent fluctuations could determine paths through the urban landscape defining the left and right plume edges rather than computing the center motion and spreading of a large number of puffs. This alone is a major computational saving because the edges can be integrated more accurately at less cost when the hazard areas are computed directly. There is an additional major saving that this alternate approach makes possible. All plume edge paths, since they depend on the underlying wind and turbulence fields that have been pre-computed, can also be pre-computed, tabulated, and stored for instant look-up. Nomografs record these limiting left and right plume edge paths in a very compact data structure that serves for all source locations within the urban “canopy,” (i.e. near the ground).
The following is a discussion of the approximations which make this plume edge approach, as implemented in nomografs, efficient and effective. Please remember that the accuracy of the winds fields used determines the accuracy of the contaminant plume regardless of the computer algorithms used. This was discussed above with regard to the importance of accurate terrain and accurate building geometry. The fluid-dynamic principles that are central to the current DISPERSION NOMOGRAFS representation and its subsequent applications are stated in P1. through P4. as follows:
P1. A contaminant transports dynamically via convection with the local air velocity; this is not diffusion. All relevant transport and dispersion arises from resolved (and possibly unresolved) fluid motions. Diffusion, per se, plays only a minimal role.
P2. Vertical spreading of contaminant is quick on the building scale in an urban environment. Both simulations and field trials support this observation, allowing a two-dimensional computation of the hazard “area” as a footprint for a fully three-dimensional plume representation.
P3. Maximum lateral dispersion of contaminants occurs near the ground because the buildings cause strong transverse turbulence down where the average wind speed is relatively slow. As a result, the direction of the asymptotic plume edges is determined entirely locally with no need to know where the source is. The further spreading of any small parcel of contaminant that arrives at a location only depends on what happens there.
P4. Wherever the contaminant goes becomes contaminated and a volume, once contaminated, stays contaminated. This is a conservative approximation favored by first responders to aid in “safe siding” the predictions. It could (perhaps) be relaxed considerably for applications in open regions or over water.
Because fluid dynamic turbulence is not diffusion (Principle P1), plume edges are actually quite sharp, not fuzzy as assumed with puffs, but the actual location of this sharp edge can be rather uncertain. We may not be able to predict exactly where the edge of the plume is at any instant and we call this variability—but the edge at any instant will be quite sharp. FIG. 10A, FIG. 10B, FIG. 10C, FIG. 10D, FIG. 10E, FIG. 10F, FIG. 10G, FIG. 10H and FIG. 10L below show eight different plumes computed 20 minutes after an SF6 trial release over downtown Los Angeles using the same input winds and weather. Each of these instantaneous plume snapshots has a quite sharp edge although the overall plume shapes are noticeably different.
Eight different plumes result because the local wind fluctuations were all somewhat different because the contaminant clouds were released at eight different times. These are called different “realizations” and a very important conclusion is that there is no one single “unique” answer. No one of these realizations is more accurate or more “correct” than any other.
As indicated above, FIG. 10A, FIG. 10B, FIG. 10C, FIG. 10D, FIG. 10E, FIG. 10F, FIG. 10G, FIG. 10H and FIG. 10L illustrate eight different realizations computed for a single source. These are compared with Tracer ES&T sampler data from downtown Los Angeles (squares). The wind is from 170° at 3 m/s with moderate fluctuations. The point releases are 5 min in duration with measurements (2.5 min sampling intervals) at each of 50 locations within about 1 km source at the lower circle/dot at the bottom of FIG. 10L. Estimating variability requires multiple trials. There is no correct or “unique” answer!
Another important fluid dynamic consideration in using plume edges paths (nomografs) to determine a hazard area is to decide that a point stays contaminated once it has been contaminated (Principle P4.). In light of the essentially unpredictable variations shown in FIG. 10A through FIG. 10H and FIG. 10L, the safest approach is to take the worst of the realizations as defining the “envelope,” the outer boundary, of the hazard area. FIG. 11A, FIG. 11B, FIG. 11C and FIG. 11D show plume envelope construction schematically at a particular time after the contaminant release begins, shown as four different light shaded plumes, labeled (a) to (d). Each is a possible realization of the plume from the source at the red circle. The dark shaded circumferential “envelope” drawn in behind each of these realizations is the ideal hazard area we would like to predict if these four realizations were the only possible solutions. Each plume fills out a different fraction (percentage) of the composite hazard area and there is a probability that each point in the hazard will be contaminated by any particular realization.
Thus, FIG. 11A. FIG. 11B. FIG. 11C and FIG. 11D illustrate four different plume realizations (light shaded areas) of a single source are overlaid on the plume envelope, here defined as the union of all these plume realizations. Since there is no one “correct” answer, the plume envelope gives a hazard area that evolves in time and generally provides a safe, conservative estimate of the area that could be contaminated.
The concept of a two-dimensional plume envelope is useful because the maximal lateral spreading of the plume is determined near the ground (Principle P2.) and this lateral extent is not very different up to the average height of the buildings (Principle P3.). This construct “safe sides” the predicted hazard area because it is not based on an average of the realizations, as with most Gaussian averaging models, but rather is the union of worst cases. The probability that any particular location outside the plume envelope will be contaminated at time t will be small and can be made smaller by making the plume envelope a little bit larger.
V. Computing Limiting Plume Envelope Edges: DISPERSION NOMOGRAFS
This new approach, to find the limiting plume envelope edges directly, is both safer and faster. The main limitation is that the prediction will be confined to the domain where the CFD computations for the nomografs have been performed and to sources within the urban canopy (i.e. near the ground). Nomografs for areas as large as 40 km by 30 km have been computed and methods exists to extend the nomograf approach to long-time variations in the winds but the predictions are generally limited to an hour or two, unless the winds are quite steady, and to the first 10- to 20 kilometers downwind of the source.
When an agent density (concentration) is desired, a simple polynomial profile is interpolated into the three-dimensional extension of the plume envelope above the surface. Our algorithms use the DISPERSION NOMOGRAFS tables to determine the spatial distribution of the agent density within the plume envelope. In this way only one simple polynomial evaluation is computed at each point inside the plume envelope and none are performed outside the envelope. Meanwhile, the nomografs transfer information about the local geometry into the approximate density profiles. This approach implicitly depends on principles P2. and P3. stated above.
To summarize this new approach schematically, look at FIG. 12 below. The limiting left plume edge is computed by integrating along a direction given by taking the average wind direction near the ground and deflecting this direction to the left by the strength of the fluctuations. On the upper blue curve, labeled “left edge” in the figure, a black arrow in the local average wind direction is shown. The blue wedge at this location indicates the left and right fluctuations of the wind velocity that go into building up this average wind direction. It is clear that a different right edge can be started at each point along the left edge. The limiting right plume edge that originates at the right (lower) edge of the source is determined just as the left edge is and diverges to the right of the left edge by an amount that depends on the local fluctuations divided by the average wind speed. It is also clear that a new left edge could be started at each point along the chosen right edge.
FIG. 12 illustrates the result of computing left and right plume edges to bind the transport and dispersion of a contaminant. Individual components (puffs) in the Gaussian puff method are shown in grey to indicate the relationship between the different approaches.
FIG. 12 also shows a red line used to cap off the plume envelope at any particular time. The distance of this end cap from the source depends on the time that has elapsed after the release has begun and the distribution of wind speeds over the domain. It should be obvious that these edge integrals could be performed for each source scenario separately and the resulting hazard area prediction would be a lot faster than current methods and more accurate, as long as detailed, pre-computed wind and turbulence fields are used.
As mentioned above, however, P1. and P3. taken together, mean that the limiting left and right edge directions for a small parcel of contaminant near the ground, at any place in the domain, cannot depend on where that parcel came from. As a result, the limiting left and right edges extend all the way across the domain and only need to be computed once and stored. This is what DISPERSION NOMOGRAPS are designed to do (FIG. 13 below). The nomografs are contour maps of the domain, one for the right edges and one for the left, where the edges originating at a location (xs,ys) are defined by the contour levels R(x,y)=R(xs,ys) and L(x,y)=L(xs,ys).
This definition is “Gauge invariant” mathematically, meaning that the particular “height” values used to label the contours are irrelevant, only the geometry of the limiting plume edge curves through the domain matters. In this approach, given a source location, we can look up the plume edges directly from the nomografs so the procedure is very fast! The nomografs can encode very accurate edge shapes and each left and right edge contour can be used for many sources. Therefore the representation is very compact as well as very fast to apply. Calculation times for hazard areas take only a few tens of milliseconds with accurate edge shapes and computing a density profile inside the plume envelope takes only two or three times longer.
FIG. 13 below indicates schematically how the same left and right edge contours can be used, even simultaneously, for multiple sources. For simplicity a single limiting left edge contour (thicker blue line) and a limiting right edge contour (thicker black line) have been duplicated above and below to show what an idealized nomograf would look like. A situation exactly like this would occur if the average wind direction and the corresponding turbulence fluctuation strength were to depend only on the horizontal coordinate (x) but not the vertical coordinate (y).
FIG. 13. Left edges (i.e., plume edge paths depicted by lines illustrated at the top half of FIG. 13) and right edges (i.e., plume edge paths depicted by lines illustrated at the bottom half of FIG. 13) limiting plume edge paths can be nested into a data structure containing two contour maps as shown. Because the contaminant plume edge directions are determined near the ground, this direction is the same whether near the source, in the middle of the plume, or near the downwind boundary. Three plume envelopes are shown.
Even though the wind fields leading to FIG. 13 are constrained and artificial, we can still see that plumes originating in different places have different shapes. The dark shaded circles indicate three source locations. The source on the left side of FIG. 13 shares its right edge with the lower source and shares its left edge with the upper source so the resulting larger shaded plume envelope would eventually spread to cover the other two plumes in the upper middle and on the right. In this figure, the source on the left has been active for twice as long as the upper source and about three times as long as the lower (rightmost) source.
VI. Computing DISPERSION NOMOGRAFS from FAST3D-CT Runs
The data collected for nomograf generation in a FAST3D-CT urban aerodynamics simulation include:
D1. The three-dimensional means and standard deviations of the three velocity components of the airflow computed from data collected at seven ground-conforming height levels from the ground to above the height of the typical buildings. This collection covers an interval of at least 30 minutes and often an hour after a run initiation “spin-up” period.                D1a. Average over the collection interval of the X- Y- and Z-components of the air velocity at the seven chosen heights.        Dab. Standard deviations of the wind velocity components around the average values at the seven heights measuring both resolved fluctuations and turbulence.        
D2. Six key quantities are accumulated at two different heights for each of a number of sources that are initialized after the CFD model “spin-up” period is complete and the statistics of the fluctuation urban aerodynamics have stabilized.                D2a. First arrival time (sec) of contaminant density exceeding a threshold value at each location,        D2b. Time of arrival (sec) of the maximum contaminant value at the location,        D2c. Decay time (sec) after the maximum is reached at the location,        D2d. Local peak contaminant density (gm/m3) at any time,        D2e. Integrated contaminant density at the location (dose=sec gm/m3),        D2f. Local contaminant variability, measured as the integrated total variation (gm/m3).        
A typical run with the FAST3D-CT model for a complex urban area of 30 square km resolved with 6 m cells takes 12 hours on a 16-processor Silicon Graphics Inc. (“SGI”) computer system. This is significantly faster per square km than classical CFD models due to the savings achieved by our MILES turbulence model, our efficient treatment of the complex geometry, and other algorithmic improvements including efficient parallel processing. Because of the FAST3D-CT model efficiency, we can compute a set of DISPEERSION NOMOGRAFS for each eighteen different wind directions in a few days of computing on what is really a rather modest “supercomputer.”
The right and left DISPEERSION NOMOGRAFS edge contours are computed geometrically by integrating along the right and left edge directions as constructed in FIG. 7B, i.e., in the panel on the right. The actual computational procedure is very similar to computing a stream function for a potential flow problem by integrating along the steady streamlines. Right edges cannot cross or join each other in nomografs. Similarly the left edges cannot cross or join each other. The actual direction for the edge contour at a point is computed as a weighted average of the local wind velocity components (D1a) plus (right) and minus (left) the standard deviations (D1b) over the seven height levels recorded in D1 above. The heaviest weighting is at or below the height of the typical buildings, as required by principles P2. and P3. above.
While the nomografs themselves depend only on the geometric velocity data, the data items in D2 are used to calibrate the scale factor that multiply the standard deviations (arcs) in FIG. 7A and FIG. 7B. Thus this scale factor controls the overall left and right deflections of the plume edges from the average wind direction; the calibration with the FAST3D-CT items in D2 ensures the overall dispersion encoded in the nomografs agrees with the CFD simulations. These D2 data are also used to calibrate the formulae and interpolations used by CT-ANALYST to convert the nomograf edge contours to on-screen predictions. Not coincidentally, the quantities indicated in D2 are virtually the same definitions and are computed exactly as for the short-duration releases in the Hamburg wind tunnel in the recent FAST3D-CT validation projects using Oklahoma City trials and matching wind tunnel studies. Thus there is a rather direct trail from the experiments and the data taken there directly through the detailed CFD simulations to the CT-Analyst predictions.
Speaking on a more operational level, the four steps in generating and using DISPEERSION NOMOGRAFS for a city are:
1. An accurate geometry database is compiled from Light Detection & Ranging (“LIDAR”), stereo imagery, or shape files. The geometry database used by FAST3D-CT is a two-dimensional (typically one meter resolution) array that returns the heights of terrain, buildings, and trees, and surface composition in the computational domain. Other, more complex forms can be used and reduced to the required FAST3D-CT input.
2. Detailed 3D computational fluid dynamics calculations (FAST3D-CT) are repeated for 18 wind directions spaced 20 degrees around the compass and the results for each run are captured in an extensive database. These simulations include the appropriate urban boundary layer for the region with realistic turbulent fluctuations imposed at the inflow boundaries. Multiple releases are tracked in each case as described above.
3. The salient features from the CFD database are distilled into DISPEERSION NOMOGRAF plume edge contour maps for rapid interactive access. The nomografs primarily capture how the local building geometry affects the shape of the plume envelopes. Time integration is thus replaced by interpolations that capture the aerodynamic effects of the full urban geometry.
4. The nomograf tables then are encrypted and input to the CT-ANALYST software, an easy-to-use graphical user interface (GUI) for instantaneous situational analysis. Plume computation, for example, takes less than 50 milliseconds. An actual example is shown in the next section below.
FIG. 14A and FIG. 14B below show an example of the left and right edge nomograf tables for a small island domain with the wind from the north (top). The grayscale shading coding of the left edge nomograf (FIG. 14A) and the right edge nomograf (FIG. 14B) shows that these two arrays are indeed contour maps with darker shading in FIG. 14A indicating low (negative) values and lighter shading indicating larger (positive) values (see FIG. 14B). The broad lines, alternating light and dark shading in FIG. 14A and FIG. 14B, identify a few of the limiting plume envelope edge contours. The width of these lines indicates qualitatively the spreading which a parcel of contaminant would undergo at that location. This visualization helps show the relationship of large lateral dispersion of the plume edges, and therefore also in the contaminant plumes, to the underlying geometry. The higher and denser the buildings, the more the plume edges are deflected from the mean wind direction. This figure also shows that the plume edge contours are essentially straight over flat open areas such as the water.
FIG. 14A and FIG. 14B illustrate left edge (left panel) and right edge (right panel) respectively, DISPEERSION NOMOGRAF contours for a fictitious island kingdom called Atlantis. The wind is from the top and the alternating purple and grey bands illustrate several of the nomograf plume envelope edge contours.
VII. Using DISPEERSION NOMOGRAFS: CT-ANALYST Examples
FIG. 15 uses CT-ANALYST to compute plume envelopes for two sources located at the blue stars below. These were computed using the DISPEERSION NOMOGRAF shown in FIG. 14A and FIG. 14B. The crosshatched bands can be seen to be the same as in FIG. 14A and FIG. 148 overlaid on the CT-ANALYST screenshot. FIG. 15 illustrates the relationship of plume envelopes and contamination footprints to the underlying DISPEERSION NOMOGRAF.
FIG. 15 illustrates two distinct plume envelopes from CT-ANALYST which are shown in relationship to the underlying nomograf edge contours. The plume footprints, shown in solid grey behind the plume envelopes, are defined (downwind) exactly as filling the region between the left and right plume edge contours.
FIG. 16 below shows the entire CT-ANALYST interactive control screen for an urban area, in this case a section of downtown Washington D.C. prepared to support the 2005 and 2009 inaugurations. The contaminant concentration display (varying shades of shaded contours) for the source at the star (at the bottom of the FIG. 16) is overlaid on the contamination footprint (shaded gray region). Star-shaped nodes are sources, triangular and circular nodes are sensor reports, and square nodes indicate specific sites. When a source node is active it is illustrated with light shading. Footprints, plume envelopes, contaminant concentration plots, and escape routes can be displayed for sources by activating buttons on the lower portion of the CT-ANALYST screen. Triangular sensor report nodes inside an active plume envelope are “hot” (SOLID SHADING) while those still uncontaminated are “cold” (light shaded triangle within the shaded triangle). In this example all the site displays are inactive as shown by the buttons. Downwind consequence regions (for active “hot” reports) and upwind backtrack estimates (for all active “hot” and “cold” reports) can be displayed for individual sensor nodes, indicated by filled triangles. Contamination zones from downwind leakage and upwind danger zones can be plotted for all square site nodes (light shaded when they are active). The diagonal shaded lines are the recommended evacuation (escape) routes.
FIG. 16 is a CT-ANALYST full screen shot showing contaminant density contours the contamination footprint, and evacuation routes overlaid on a Washington D.C. city map. The wind is from the southeast. Evacuation routes are optimized to minimize inhaled contaminant doses. The dark region in the lower middle of the display is the result of the CT-ANALYST backtrack operation. Several “hot” sensors and two “cold” sensors were used to “backtrack” to a source location estimated using a union of the upwind “danger zone” capability.
To compute displays such as danger zones, plume envelopes, and backtracks to unknown source locations, knowing the actual concentration of the airborne agent is not necessary. Indeed, until the total amount of the contaminant is known, plotting the actual concentration distribution isn't even possible. Therefore, CT-ANALYST provides a relative concentration until the mass of the agent from a specific source can be estimated. Fortunately, this relative concentration and its time history are all that is needed to select civil defense options that minimize the inhaled dose of contaminant. The normalization used for FIG. 10 was chosen to correspond to the integrated mass of the source used in the corresponding FAST3D-CT simulations used to develop the nomografs. This normalization also accounts for the contaminant that leaves the grid through an analytic extension of the nomograf data arrays.
The two panels in FIG. 17A and FIG. 17B below were taken from cropped CT-ANALYST screen shots for a region in downtown Washington D.C. using two different nomograf tables. Panel (a) (FIG. 17A) shows three different nomograf-based displays computed 6 minutes after a release has occurred at the source indicated by the light blue star using nomografs that encode the actual detailed Washington D.C. geometry resolved to 1-meter accuracy. The source of contamination may be an accident, a leaking sprayer, or a broken container of hazardous chemicals that needs to be analyzed. Panel (b) (FIG. 17B) shows the corresponding predictions when the detailed geometry is ignored. The closed pink contour in each panel shows the 6-minute plume envelope when the wind is 3 meters per second from the west-northwest. The plume envelopes show the geographical region that the contaminant plume could have reached during its expansion up to the indicated time after release. The corresponding contamination footprints (grey) behind the plume envelope in FIGS. 11a and 11b respectively, represent the full extent of the growing contamination region after the plume envelope has spread to its maximum toxic extent. The actual contaminant plume envelope starts at the source near the upwind corner of the footprint and expands downwind away from the source as time increases.
FIG. 17A and FIG. 17B illustrate DISPEERSION NOMOGRAFS in CT-ANALYST capture building aerodynamics. a) Nomograf results with full building geometry. b) Nomograf computed excluding buildings, trees, and terrain. The figure shows the corresponding contamination footprints (darker gray), plume envelopes after 6 minutes (lighter gray), and the upwind danger zone of a site (grayscale in the upper left corners of FIG. 17A and FIG. 17B).
The plume envelope and contamination footprint in Panel (b) see (FIG. 17B) are computed in exactly the same way as in Panel (a) (see FIG. 17A) except that the geometry used for the nomografs is flat and featureless. As a result the plume envelope is symmetric, exactly wind aligned, and shows none of the local dispersion caused by the actual building complexes whose effects are illustrated in Panel (a). Such a simple, non-physical result would be expected from Gaussian puff models using average roughness coefficients and even from Gaussian plume models. The results, however, are wrong. Even a quick look at such results displayed generally makes most people suspicious.
The shaded regions in FIG. 17A and FIG. 17B show estimations of the upwind danger zone for the chosen site (bright square) with and without capturing the effects of the geometry, respectively. The danger zone for a site is the set of all possible positions upwind where a source of contamination could reach the site. Computing the danger zone is an entirely new capability made possible by the nomograf representation and algorithms. Notice the difference caused by the local variations of the city geometry. In (b) (i.e., FIG. 17B), without proper representation of the geometry, the source (shaded star) is outside the predicted danger zone (dark shaded) and the plume envelope (lighter shaded) areas and therefore does not reach the site. In (a) (i.e., FIG. 17A) however, the extra northward dispersion from the buildings causes the plume envelope to reach the green square (site). In turn, CT-ANALYST shows, via the danger zone, that the given site can be threatened from the location of the star. Clearly the predictions using the correct geometry are “safer.”
Sensors are indicated in these figures with triangular icons. Shaded sensor icons have not been triggered by contaminant at the time depicted in FIG. 17A and FIG. 17B, as they lie outside of the instantaneous plume envelope. Some sensors and sites will lie outside the footprint with flat-earth geometry but inside the footprint when full geometry is used. In other words, a prediction that does not account for complex geometry gives a false negative result for many locations, possibly resulting in unnecessarily high losses. An emergency response tool that does not account for complex geometry will be unreliable at best. Some conventional plume software greatly overestimates the size of a plume envelope, particularly near the source, to avoid these geometry-induced false negatives. Severe overestimates can also have dangerous consequences. People may be inclined to stay in a dangerous location, thinking an uncontaminated region is too far away to reach.
VIII. Summary:
All methods to compute the transport and dispersion of airborne contaminants need to use a representation of the wind field over the region of interest. Only when this representation of the wind field is accurate can the plume prediction be reliable. Providing an accurate, building-scale approximation of the wind field is a slow, costly computational process, far too slow for emergency applications while the responsible officials (users) wait. Therefore conventional CT models generally use unresolved constant parameter winds (for Gaussian plume models), very poorly-resolved wind field estimates that they can get quickly from other sources (for Gaussian puff models), or possibly phenomenological wind/building interaction models (for Lagrangian particle models). These models still do a lot of computing while the users wait, eventually arriving at hazard-area predictions after several minutes that have obvious inaccuracies and other limitations.
In these earlier rather inaccurate, city-scale predictions, the specification of atmospheric stability classes and many other global properties about the agents and source dispersion mechanisms fosters a kind of intellectual misrepresentation that misleads users, projecting a false sense of reliability for the models. For example, specifying the temperature and pressure of a toxic agent like chlorine and then asking a user to state the size hole that the chlorine is coming out of gives the impression that the heavier-than-air aspects of the release are being properly accounted for. Actually the type of surface, such as sand, water, or concrete, its heat transfer properties, and the slope of the terrain are even more important and yet totally neglected.
By way of contrast, this discussion shows that the hazard area of a CT scenario can be computed quickly, accurately, and directly using detailed, pre-computed wind fields that properly capture individual building effects. This approach leads to a very efficient representation in terms of DISPERSION NOMOGRAFS where the plume envelope edges are recalled from compact, contour-map databases. In our implementation a state-of-the-art CFD model, FAST3D-CT, pre-computes the complete time-dependent 3D urban aerodynamics with full urban geometry at high resolution (2-6 meters). In this way there is no operator delay in using the very best wind velocity fields available. DISPERSION NOMOGRAFS recall the results of these high-resolution 3D simulations with no time delay for transport and dispersion (T&D) calculations of many puffs/particles over many time steps.
The instant response CT-ANALYST format using nomografs also allows quick sensor fusion operations and permits users to “backtrack” to unknown source locations with actionable information in a few milliseconds. DISPERSION NOMOGRAFS are faster because they provide plume edges directly rather than computing them laboriously while the user waits. This approach is more accurate primarily because there is no user delay in using the very best wind velocity fields that can be had. CT-ANALYST is also more robust because there is essentially no computation to go bad, very little input is needed, and the displays are intuitive. The software that is easier to use because it is simpler.
Contemporary common-use hazard prediction and consequence assessment systems:
Contemporary common-use hazard prediction and consequence assessment systems have at their heart a plume simulation model based on a Gaussian plume/puff model. These systems typically employ Gaussian plume simulation models. The Gaussian plume method, while relatively fast, tends to be inaccurate, especially for urban areas. The setup for all these systems tends to be complicated, and require prior knowledge of the source characteristics.
Some examples of common-use hazard prediction and assessment systems are as follows:
CATS (Consequences Assessment Tool Set) is a consequence management tool package, developed by the U.S. Defense Threat Reduction Agency, U.S. Federal Emergency management Agency, and Science Applications International Corp, that integrates hazard prediction, consequence assessment, emergency management tools, including the Hazard Prediction and Assessment Capability (HPAC) system, and critical population and infrastructure data within a commercial Geographical Information System. (CATS: Consequences Assessment Tool Set, U.S. Defense Threat Reduction Agency, U.S. Federal Emergency management Agency, and Science Applications International Corp.; SWIATEK et al. “Crisis Prediction Disaster Management”, SAIC Science and Technology Trends II, Jun. 24, 1999).
CAMEO® (Computer Aided Management of Emergency Operations) is a system of software applications used to plan for and respond to chemical emergencies. It is one of the tools developed by EPA's Chemical Emergency Preparedness and Prevention Office (CEPPO) and the National Oceanic and Atmospheric Administration Office of Response and Restoration (NOAA), to assist front-line chemical emergency planners and responders. (CAMEO: Computer Aided Management of Emergency Operations, EPA's Chemical Emergency Preparedness and Prevention Office (CEPPO) and NOAA; CAMEO “Computer Aided Management of Emergency Operations,” U.S. Environmental Protection Agency, May 2002, pp. 1-306).
MIDAS-AT™ (Meteorological Information and Dispersion Assessment System —Anti-Terrorism), a product of ABS Consulting Inc. is a software technology that models dispersion of releases of industrial chemicals, chemical and biological agents, and radiological isotopes caused by accidents or intentional acts. MIDAS-AT is designed for use during emergencies and for planning emergency response drills. Its Graphical User Interface (GUI) is designed for simple entry of information required to define a terrorist scenario (MIDAS-AT Meteorological Information and Dispersion Assessment System—Anti-Terrorism: ABS Consulting).
HPAC (Hazard Prediction and Assessment Capability), developed by the Defense Threat Reduction Agency, is a forward-deployable, counter proliferation-counterforce collateral assessment tool. It provides a means to predict the effects of hazardous material releases into the atmosphere and its impact on civilian and military populations. The HPAC system also predicts approximate downwind hazard areas resulting from a nuclear weapon strike or reactor accident and has the capability to model nuclear, chemical and biological weapon strikes or accidental releases. (HPAC: Hazard Prediction and Assessment Capability, DTRA, HPAC Version 2.0 and HASCAL/SCIPUFF Users Guide, Defense Special Weapons Agency, July 1996; “Hazard Prediction and Assessment Capability” Fact Sheet, Defense Threat Reduction Agency Public Affairs, pp. 1-2).
VLSTRACK (Vapor, Liquid, and Solid Tracking), developed by Naval Surface Warfare Center, provides approximate downwind hazard predictions for a wide range of chemical and biological agents and munitions of military interest. The program features smart input windows that check input parameter combinations to ensure that a reasonable attack is being defined, and simple and informative output graphics that display the hazard footprint for agent deposition, dosage, or concentration. The model also features variable meteorology, allowing for interfacing the attack with a meteorological forecast. (VLSTRACK: Vapor, Liquid, and Solid Tracking, [U.S. Pat. No. 5,648,914] Naval Surface Warfare Center, Bauer, T. J. and R. L. Gibbs, 1998, NSWCDD/TR-98/62, “Software User's Manual for the Chemical/Biological Agent Vapor, Liquid, and Solid Tracking (VLSTRACK) Computer Model, Version 3.0,” Dahlgren, Va.: Systems Research and Technology Department, Naval Surface Warfare Center).
ALOHA (Areal Locations of Hazardous Atmospheres), from EPA/NOAA and a component of CAMEO, is an atmospheric dispersion model used for evaluating releases of hazardous chemical vapors. ALOHA allows the user to estimate the downwind dispersion of a chemical cloud based on the toxicological/physical characteristics of the released chemical, atmospheric conditions, and specific circumstances of the release. Graphical outputs include a “cloud footprint” that can be plotted on maps to display the location of other facilities storing hazardous materials and vulnerable locations, such as hospitals and schools. (ALOHA®—Arial Locations of Hazardous Atmospheres, EPA/NOAA; “ALOHA Users Manual”, Computer Aided Management of Emergency Operations, August 1999, pp. 1-187).
FASTD-CT (FAST3D—Contaminant Transport) is a time-accurate, high-resolution, complex geometry CFD model developed by the Laboratory for Computational Physics and Fluid Dynamics at the Naval Research Laboratory. The fluid dynamics computations are performed with a fourth-order accurate implementation of a low-dissipation algorithm that sheds vortices from obstacles as small one cell in size. Particular care has been paid to the turbulence treatments since the turbulence in the urban canyons lofts ground-level contaminant up to where the faster horizontal airflow can transport it downward. FAST3D-CT has a number of physical processes specific to contaminant transport in urban areas such as solar chemical degradation, evaporation of airborne droplets, re-lofting of particles and ground evaporation of liquids. (FAST3D-CT: FAST3D—Contaminant Transport, LCP & FD, NRL Boris, J. “The Threat of Chemical and Biological Terrorism: Preparing a Response,” Computing in Science & Engineering, pp. 22-32, March/April 2002).
NARAC (National Atmospheric Release Advisory Center) maintains a sophisticated Emergency Response System at its facility at Lawrence Livermore National Laboratory. The NARAC emergency response central modeling system consists of a coupled suite of meteorological and dispersion models. Users access this system using a wide variety of tools, also supplied by NARAC. Users must initiate a problem through a phone call to their operations staff or interactively via computer. NARAC will then execute sophisticated 3-D models to generate the requested products that depict the size and location of the plume, affected population, health risks, and proposed emergency responses. (NARAC: Atmospheric Release Advisory Capability, Lawrence Livermore National Laboratory, “Forewarning of Coming Hazards,” Science & Technology Review, pp. 4-11, June 1999, Lawrence Livermore National Laboratory).
Contemporary tools, such as the FASTD-CT: FAST3D-CT and NARAC, capable of providing engineering-quality 3D predictions are reliable, but they take a long time, i.e., hours and/or days to set up, run and analyze, before results are returned.
All of the above-mentioned systems take several minutes, hours, or even days to return results. Simplified systems such as PEAC® (Palmtop Emergency Action for Chemicals) [U.S. Pat. No. 5,724,255], originally developed by Western Research Institute, provide the necessary emergency response information to make quick and informed decisions to protect response personnel and the public. PEAC-WMD 2002 provides in hand information compiled from a number of references with very fast recall. PEAC provides emergency responders with instant access to information from a number of sources and evacuation distances based on several sets of guidelines. This system, can return results within seconds and requires less detailed knowledge of the source, but the resulting fixed-shape plume does not take into account any effect of complex terrain or buildings.
Waiting even one or two-minutes for each approximate scenario computation can be far too long for timely situation assessment as with contemporary common-use hazard prediction systems. Overly simplified results can result in inaccurate results. The answer to this dilemma is to perform the best computations possible from state-of-the-art 3D simulations well ahead of time and capture their salient results in a way that can be recalled, manipulated, and displayed instantly.
In many emergency response scenarios, in addition to knowing the severity of the effects, it is important to know how much time is available before any deleterious effects will occur. The time required for the plume to reach a given location, the arrival time, will influence the response: ranging from a simple shelter-in-place to outright evacuation. While most of the contemporary models described are capable of calculating the arrival time of a contaminant, they typically present this information inefficiently. For example the predictions of a plume at 5, 15, 30 and 60-minute after release are presented to the user as four separate images, and the arrival time at a specific site cannot be determined.
Therefore, the need exists for a software emergency assessment tool which is easy to use and effective instantaneously providing immediate assessment of new data, instantaneous computations of exposed and soon-to-be exposed regions, and the zero-delay evaluations of options for future actions. The software should also be capable of projecting optimal evacuation paths based on the current evolving situation assessment.
Further, the need exists for a new tool which is much faster than contemporary “common use” models with accuracy comparable to three-dimensional, physics-based flow simulations for scenarios involving complex and urban landscapes. The focus is on situation assessment through sensor fusion of qualitative and incomplete data.
Further, the need exists for a solution to the current inefficient attempts of detailing the severity of contaminant effects, by providing a unified display which efficiently depicts the contaminant severity elements along with additional components which are invaluable when making decisions where lives are at risk.